Abstract

Rotary axes are the key components for five-axis computerized numerical control machines, while their motions are dramatically influenced by thermal issues. To precisely model the thermal error of rotary axis, a convolutional neural network (CNN) model is developed. To form data sets for the CNN, a laser interferometer is used to measure the angular positioning error at different temperatures and a thermal imager is taken to obtain thermal images of the rotary axis. The measured thermal error is fitted to a sine curve so that training parameters are reduced. And the thermal pixel values of the initial thermal image are subtracted from all the thermal images to consider the incremental thermal effect, so the influence of the initial temperature is negligible. Finally, a deep CNN model with multiple output classifications is designed to complete the data training, verifying and testing. The experimental results show that the prediction accuracy for the parameters is higher than 90%, and the percentage reduction in error is higher than 80%.

References

1.
Mayr
,
J.
,
Jedrzejewski
,
J.
,
Uhlmann
,
E.
,
Donmez
,
M.
,
Knapp
,
W.
,
Härtig
,
F.
,
Wendt
,
K.
,
Moriwaki
,
T.
,
Shore
,
P.
,
Schmitt
,
R.
,
Brecher
,
C.
,
Würz
,
T.
, and
Wegener
,
K.
,
2012
, “
Thermal Issues in Machine Tools
,”
CIRP Ann.
,
61
(
2
), pp.
771
791
. 10.1016/j.cirp.2012.05.008
2.
Bryan
,
J.
,
1990
, “
International Status of Thermal Error Research (1990)
,”
CIRP Ann.
,
39
(
2
), pp.
645
656
. 10.1016/S0007-8506(07)63001-7
3.
Li
,
Y.
,
Zhao
,
W.
,
Lan
,
S.
,
Ni
,
J.
,
Wu
,
W.
, and
Lu
,
B.
,
2015
, “
A Review on Spindle Thermal Error Compensation in Machine Tools
,”
Int. J. Mach. Tools Manuf.
,
95
(
1
), pp.
20
38
. 10.1016/j.ijmachtools.2015.04.008
4.
Li
,
Z.
,
Zhao
,
C.
, and
Lu
,
Z.
,
2020
, “
Thermal Error Modeling Method for Ball Screw Feed System of CNC Machine Tools in x-Axis
,”
Int. J. Adv. Manuf. Technol.
,
106
(
11
), pp.
5383
5392
. 10.1007/s00170-020-05047-w
5.
Bitar-Nehme
,
E.
, and
Mayer
,
J. R. R.
,
2016
, “
Thermal Volumetric Effects Under Axes Cycling Using an Invar R-Test Device and Reference Length
,”
Int. J. Mach. Tools Manuf.
,
105
(
1
), pp.
14
22
. 10.1016/j.ijmachtools.2016.03.003
6.
Li
,
J.
,
Zhang
,
W.
,
Yang
,
G.
,
Tu
,
S.
, and
Chen
,
X.
,
2009
, “
Thermal-Error Modeling for Complex Physical Systems: The-State-of-Arts Review
,”
Int. J. Adv. Manuf. Technol.
,
42
(
1–2
), pp.
168
179
. 10.1007/s00170-008-1570-x
7.
Liu
,
H.
,
Miao
,
E.
,
Wei
,
X.
, and
Zhuang
,
X.
,
2017
, “
Robust Modeling Method for Thermal Error of CNC Machine Tools Based on Ridge Regression Algorithm
,”
Int. J. Mach. Tools Manuf.
,
113
(
1
), pp.
35
48
. 10.1016/j.ijmachtools.2016.11.001
8.
Gebhardt
,
M.
,
Mayr
,
J.
,
Furrer
,
N.
,
Widmer
,
T.
,
Weikert
,
S.
, and
Knapp
,
W.
,
2014
, “
High Precision Grey-Box Model for Compensation of Thermal Errors on Five-Axis Machines
,”
CIRP Ann.
,
63
(
1
), pp.
509
512
. 10.1016/j.cirp.2014.03.029
9.
Mayr
,
J.
,
Egeter
,
M.
,
Weikert
,
S.
, and
Wegener
,
K.
,
2015
, “
Thermal Error Compensation of Rotary Axes and Main Spindles Using Cooling Power as Input Parameter
,”
J. Manuf. Syst.
,
37
(
1
), pp.
542
549
. 10.1016/j.jmsy.2015.04.003
10.
Mayr
,
J.
,
Blaser
,
P.
,
Knapp
,
W.
, and
Wegener
,
K.
,
2016
, “
Compensation of Cutting Fluid Influences on Five Axis Machine Tools
,”
The Proceedings of MTTRF 2016 Annual Meeting. MTTRF
,
San Francisco, CA
,
July 6–7
, pp.
101
118
.
11.
Ibaraki
,
S.
, and
Ota
,
Y.
,
2014
, “
A Machining Test to Calibrate Rotary Axis Error Motions of Five-Axis Machine Tools and Its Application to Thermal Deformation Test
,”
Int. J. Mach. Tools Manuf.
,
86
(
1
), pp.
81
88
. 10.1016/j.ijmachtools.2014.07.005
12.
Mou
,
J.
, and
Liu
,
C.
,
1995
, “
An Adaptive Methodology for Machine Tool Error Correction
,”
ASME J. Eng. Ind.
,
117
(
3
), pp.
389
399
. 10.1115/1.2804345
13.
Blaser
,
P.
,
Pavliček
,
F.
,
Mori
,
K.
,
Mori
,
K.
,
Mayr
,
J.
,
Weikert
,
S.
, and
Wegener
,
K.
,
2017
, “
Adaptive Learning Control for Thermal Error Compensation of 5-Axis Machine Tools
,”
J. Manuf. Syst.
,
44
(
1
), pp.
302
309
. 10.1016/j.jmsy.2017.04.011
14.
Bitar-Nehme
,
E.
, and
Mayer
,
J. R. R.
,
2018
, “
Modelling and Compensation of Dominant Thermally Induced Geometric Errors Using Rotary Axes’ Power Consumption
,”
CIRP Ann.
,
67
(
1
), pp.
547
550
. 10.1016/j.cirp.2018.04.080
15.
Gebhardt
,
M.
,
Ess
,
M.
,
Weikert
,
S.
,
Knapp
,
W.
, and
Wegener
,
K.
,
2013
, “
Phenomenological Compensation of Thermally Caused Position and Orientation Errors of Rotary Axes
,”
J. Manuf. Process.
,
15
(
4
), pp.
452
459
. 10.1016/j.jmapro.2013.05.007
16.
Fukushima
,
K.
,
1980
, “
Neocognitron: A Self-organizing Neural Network Model for a Mechanism of Pattern Recognition Unaffected by Shift in Position
,”
Biol. Cybern.
,
36
(
4
), pp.
193
202
. 10.1007/BF00344251
17.
Schmidhuber
,
J.
,
2015
, “
Deep Learning in Neural Networks: An Overview
,”
Neural Networks
,
61
(
1
), pp.
85
117
. 10.1016/j.neunet.2014.09.003
18.
Wen
,
L.
,
Li
,
X.
,
Gao
,
L.
, and
Zhang
,
Y.
,
2018
, “
A New Convolutional Neural Network-Based Data-Driven Fault Diagnosis Method
,”
IEEE Trans. Ind. Electron.
,
65
(
99
), pp.
5990
5998
. 10.1109/TIE.2017.2774777
19.
Ibaraki
,
S.
,
Oyama
,
C.
, and
Otsubo
,
H.
,
2011
, “
Construction of an Error Map of Rotary Axes on a Five-Axis Machining Center by Static R-Test
,”
Int. J. Mach. Tools Manuf.
,
51
(
3
), pp.
190
200
. 10.1016/j.ijmachtools.2010.11.011
20.
He
,
Z.
,
Fu
,
J.
,
Zhang
,
L.
, and
Yao
,
X.
,
2015
, “
A New Error Measurement Method to Identify All Six Error Parameters of a Rotational Axis of a Machine Tool
,”
Int. J. Mach. Tools Manuf.
,
88
(
1
), pp.
1
8
. 10.1016/j.ijmachtools.2014.07.009
21.
Su
,
Z.
,
Qiu
,
Z.
,
Wang
,
C.
, and
Li
,
X.
,
2015
, “
A New Method for Circular Grating's Eccentricity Identification and Error Compensation
,”
Proceedings of Fifth International Conference on Instrumentation and Measurement, Computer, Communication and Control (IMCCC)
,
Qinhuangdao, Heibei, China
,
Sept. 18–20
,
IEEE
, pp.
360
363
.
22.
Li
,
Y.
,
Hao
,
Z.
, and
Hang
,
L.
,
2016
, “
Survey of Convolutional Neural Network
,”
J. Comput. Appl.
,
36
(
9
), pp.
2508
2515
.
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